Cherry-Picking Gradients: Learning Low-Rank Embeddings of Visual Data via Differentiable Cross-Approximation

TL;DR

This paper introduces a novel end-to-end framework combining neural networks and tensor train decomposition with cross-approximation to efficiently learn low-rank embeddings of large-scale visual data from only a subset of entries.

Contribution

It presents a new adaptive sampling method integrated with neural networks for processing large, high-dimensional visual data efficiently.

Findings

Reduces data sampling complexity logarithmically with data size.

Enables processing of large-scale multidimensional grid data.

Effective for tasks requiring large receptive fields, like medical imaging.

Abstract

We propose an end-to-end trainable framework that processes large-scale visual data tensors by looking at a fraction of their entries only. Our method combines a neural network encoder with a tensor train decomposition to learn a low-rank latent encoding, coupled with cross-approximation (CA) to learn the representation through a subset of the original samples. CA is an adaptive sampling algorithm that is native to tensor decompositions and avoids working with the full high-resolution data explicitly. Instead, it actively selects local representative samples that we fetch out-of-core and on-demand. The required number of samples grows only logarithmically with the size of the input. Our implicit representation of the tensor in the network enables processing large grids that could not be otherwise tractable in their uncompressed form. The proposed approach is particularly useful for large-scale multidimensional grid data (e.g., 3D tomography), and for tasks that require context over a large receptive field (e.g., predicting the medical condition of entire organs). The code is available at https://github.com/aelphy/c-pic.